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V. K. Melnikov, “On the Stability of the Center for Time Periodic Perturbations,” Transactions of the Moscow Mathematical Society, Vol. 12, 1963, pp. 1-57.

has been cited by the following article:

• TITLE: Multi-Parameter Analysis of Optimal Transitions from Chaotic to Stable Regions for Two Classes of Systems

  AUTHORS: Yury Talagaev, Andrey Tarakanov

  KEYWORDS: Chaotic Systems; Multi-Parameter Analysis; Melnikov Method; Super-Stability

  JOURNAL NAME: Advances in Pure Mathematics, Vol.3 No.1A, January 30, 2013

  ABSTRACT: The study of the parameter space of chaotic systems is complicated by its high dimensionality (multi-parametricability). Two approaches to the study of chaotic systems are presented: multi-parameter analysis and optimal suppression of chaotic dynamics. For non-autonomous chaotic systems, this is the way to compare the effectiveness of various correction parameters that provide optimal removal of irregular dynamics. For the class of autonomous chaotic systems, this is the way to investigate the optimal conditions of super-stable behavior for the chaotic system.